Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3)⋊C9 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (#272⋊C9)⋊C2 |
| commutator, Fitting, cosocle | C2×H(3,𝔽3)⋊C9 | C22 |
| Frattini | C2×C33 | D32 |
| socle | C2×C32 | ((C3⋊D3)⋊C3)⋊C2 |
| hypocenter | H(3,𝔽3)⋊C9 | D4 |
| LCS | G ▷ C2×H(3,𝔽3)⋊C9 ▷ H(3,𝔽3)⋊C9 | |
| UCS | C1 ◁ C2 | |
277 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^5|b^2=c,e^3=g,b^a=bc,e^a=e^2g^2,f^a=f^2,g^a=g^2,h^a=h^2,d^b=d^2,f^b=f^2h,e^d=ef,f^d=fh75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 190);